Balancing coefficients

In the material balance example, the matrix B contains the material balance coefficients for the component flows based on the implicit model of the process. These adjustments can be done by hand or by... 

Multiply one or both of these numbers by factors to make electron loss equal to electron gain and then use them as balancing coefficients. 

In this formula, Qs is the balancing coefficient for the common element in the formula of the substance sought and QK is the balancing coefficient for the common element in the formula of the substance known. 

Most nuclear reactions involve breaking apart the nucleus into two or more different elements or subatomic particles. If all but one of the particles is known, the unknown particle can be determined by balancing the nuclear equation. When chemical equations are balanced, coefficients are added to ensure that there are the same number of each type of atom on both sides of the reaction arrow. To balance nuclear equations, we ensure that there is the same sum of both mass numbers and atomic numbers on both the left and right... 

The general approach for modelling catalyst deactivation is schematically organised in Figure 2. The central part are the mass balances of reactants, intermediates, and metal deposits. In these mass balances, coefficients are present to describe reaction kinetics (reaction rate constant), mass transfer (diffusion coefficient), and catalyst porous texture (accessible porosity and effective transport properties). The mass balances together with the initial and boundary conditions define the catalyst deactivation model. The boundary conditions are determined by the axial position in the reactor. Simulations result in metal deposition profiles in catalyst pellets and catalyst life-time predictions. 

Balance the following redox chemical equation. Rewrite the equation in full ionic form, then derive the net ionic equation and balance by the half-reaction method. Give the final answer as it is shown below but with the balancing coefficients. 

Alternative Forms of the Equilibrium Constant Dependence of A" on the direction of reaction and the balancing coefficients... 

Note Components are on the top row (H20 is a component but not shown) species are in the first column. Mass law equations are given across rows mole balance equations are given down columns. Where two numbers are given, the first is the mass alw exponent and the second is the mole balance coefficient. P = exp (,—F Pi/RT) is the coulombic term. Additional information on formulation of a chemical equilibrium problem in a tableau is given in Morel and Hering (reference 30). 

In a balanced equation, formulas preceded by integer balancing coefficients are used to show the same numbers of each kind of atom on... 

Of course, the key point to realize is, as was pointed out in Figure 3.6, the balancing coefficients refer to both individual chemical entities and moles of chemical entities. Thus, 2 mol of Mg and 1 mol of O2 yield 2 mol of MgO. Figure 3.7 shows this reaction from three points of view—as you see it on the macroscopic level, as chemists (and you ) can imagine it on the atomic level (darker colored atoms represent the stoichiometry), and on the symbolic level of the chemical equation. 

To conserve mass and maintain the fixed composition of compounds, a chemical equation must be balanced in terms of number and type of each atom. A balanced equation has reactant formulas on the left of a yield arrow and product formulas on the right. Balancing coefficients are integer multipliers for all the atoms in a formula and apply to the individual entity or to moles of entities. 

To construct the reaction quotient, we place the product term in the numerator and the reactant terms in the denominator, multiplied by each other, and raise each term to the power of its balancing coefficient (colored as in the equation) ... 

Check Always be sure that the exponents in Q are the same as the balancing coefficients. A good check is to reverse the process turn the numerator into products and the denominator into reactants, and change the exponents to coefficients. 

The value of is different for this equation, but the changes described in the problem have the same effects. For example, in (a), if O2 were added, the denominator of would increase, so Q. < K. As above, the reaction would proceed to the right until again. In other words, changes predicted by Le Chatelier s principle for a given reaction are not affected by a change in the balancing coefficients. 

The numbers a, b. .. andp,q. .. ensure that the equation is balanced and so are known as balancing coefficients. In practice they are usually chosen to have their smallest possible integer values, and they must be positive. Writing a chemical reaction in this way allows a quantity called the stoichiometric number to be introduced. It is given the symbol Vy (v is the Greek letter nu and Vy is pronounced nu Y ) where the subscript Y represents a given species (reactant or product) in the reaction. The stoichiometric number is then defined so that for... 

It is very important to recognize in this example that there is no simple link between the stoichiometry of the reaction and the form of the experimental rate equation. Trying to equate the partial orders of reaction for S20 and I to their balancing coefficients in the chemical equation would be similar to trying to relate apples to pears. It cannot he overemphasized that partial orders of reaction can be determined only from experimental measurements of the kinetics of a process. In the case of SiOs" turns out by coincidence, and no more than this, that the partial order has the same value as the balancing coefficient. For I , the partial order and the balancing coefficient (equal to 3) are very different. 

Ans. The balanced equation tells us that regardless of the actual amounts of reactants used, the ratios of all balancing coefficients must remain constant. We can use the ratio of moles of hydrogen to moles of nitrogen as one of several possible unit conversion factors to calculate the number of moles of hydrogen corresponding to 0.50 mol of nitrogen in this reaction ... 

Arts. In this case, we will create two conversion factors from the balancing coefficients of both reactants with that of the product and do two equivalent calculations to determine the amount of product, one based on the initial amount of N2, and the second based on the initial concentration of Hj ... 

Am. We examine the balanced equation N2 + SHj -> 2NH3. To solve this type of problem, first convert the mass of nitrogen to moles, then solve for the corresponding numbers of moles of hydrogen or ammonia using the balancing coefficients as unit conversion factors. Then finally convert back to mass, as follows ... 

An alternative method for solving this problem is to note that, since we know the formulas and molar ratios of reactants and products, we can express the balancing coefficients not only as whole numbers (moles) but also as formula masses multiplied by the balancing coefficients (the total numbers of moles of reactants and products) ... 

Ans. Yes, we can use a unit conversion factor consisting of the ratio of molar masses equal to the formula masses multiplied by the accompanying balancing coefficients ... 

Frequently, an alternate way of describing a second-order process involving two reactants is employed in which the extent of reaction, x, is used as a variable. If the reaction is one in which the balancing coefficients... 

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